Math Gk m6 Full Module

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KGR A D E

New York State Common Core

Mathematics Curriculum

GRADE K • MODULE 6

Module 6: Analyzing, Comparing, and Composing Shapes

Date: 4/11/14 i

© 2013 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Table of ContentsGRADE K • MODULE 6

Analyzing, Comparing, and Composing Shapes

Module Overview ......................................................................................................... i

Topic A: Building and Drawing Flat and Solid Shapes ............................................ 6.A.1

Topic B: Composing and Decomposing Shapes ...................................................... 6.B.1

Module Assessments ............................................................................................. 6.S.1

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Lesson


Module OverviewNYS COMMON CORE MATHEMATICS CURRICULUM K


Date: 4/11/14 ii


Grade K • Module 6

Analyzing, Comparing, andComposing Shapes

OVERVIEW

The kindergarten chapter of A Story of Units comes to a close with another opportunity for students to

explore geometry. Throughout the year, students have built an intuitive understanding of two- and three-

dimensional figures by examining exemplars, variants, and non-examples. They have used geometry as a

context for exploring numerals as well as comparing attributes and quantities. To wrap up the year, students

further develop their spatial reasoning skills and begin laying the groundwork for an understanding of area

through composition of geometric figures.

Topic A begins with students applying their knowledge of attributes to analyze two- and three-dimensional

shapes from the real world and construct models using straws and clay (K.G.5). “Let’s use the straws to make

the sides of the rectangle, and we’ll stick the straws together at each corner using clay!” Students use their

understanding of ordination to thirds to share and communicate the systematic construction of flats and

solids. “First, I cut four straws to be the same length. Second, I made a square by placing the four straws so

they look like a frame. Third, I connected the sides at the corners with four little clay balls” (K.CC.4d).

As in Module 2, students explore the relationship between flats and solids, this time using flats to build solids.

“I made my square into a cube. First, I made another square the same size. Second, I attached the two

squares with four straws the same length.” They also apply their knowledge of ordinal numbers to describe

the relative position of shapes within a set (K.CC.4d). “The yellow circle is first, and the red square is tenth.” The lessons of Topic B focus on composition and decomposition of flat shapes (K.G.6). Students begin by

using flats to compose geometric shapes. “I put two triangles together to make a square.” They then

decompose shapes by covering part of a larger shape with a smaller shape and analyzing the remaining space.

“When I cover part of my square with this triangle, I can see another triangle in the empty space.”1

As they build competence in combining and composing shapes, students build toward more complex pictures

and designs. Students progress through stages as they build competence in combining shapes to form

1 This descriptive image plus further clarification is found in the Geometry progressions document, p. 7.



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pictures: beginning with trial and error and gradually considering the systematic combination of components.

“This square fits here because the corners match the puzzle.” The culminating task of this module is set up as

a Math Olympics, a celebration of student learning from the whole year. Students complete tasks related to

number, measurement, operations, and geometry.

Composition and decomposition of geometric figures reinforce the idea that smaller units can combine to

form larger units. This concept, central to A Story of Units, underlies not only area concepts but also the base

ten number system. Students leave this module and the kindergarten year prepared to tackle the

mathematical concepts of first grade and beyond.

Focus Grade Level Standards

Count to tell the number of objects.2

K.CC.4 Understand the relationship between numbers and quantities; connect counting to

cardinality.

d. Develop understanding of ordinal numbers (first through tenth) to describe the relative

position and magnitude of whole numbers.

Analyze, compare, create, and compose shapes.3

K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay balls)

and drawing shapes.

2 Ordinality is introduced in the context of constructing and manipulating shapes. The balance of this cluster is addressed in Modules

1 and 5.3 K.G.4 is addressed in Module 2.



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K.G.6 Compose simple shapes to form larger shapes. For example, “Can you join these two triangles

with full sides touching to make a rectangle?”

Foundational StandardsPK.CC.6 Identify “first” and “last” related to order or position.

PK.G.3 Analyze, compare, and sort two- and three-dimensional shapes and objects, in different sizes,

using informal language to describe their similarities, differences, and other attributes (e.g.,

color, size, and shape).

PK.G.4 Create and build shapes from components (e.g., sticks and clay balls).

Focus Standards for Mathematical Practice

MP.1 Make sense of problems and persevere in solving them. Students persist in their use of trial

and error until they begin to use the attributes of a puzzle to determine which shape fits into

an open space. “The empty space has a long side like my triangle. Let’s see if my triangle

fits.”

MP.4 Model with mathematics. Students use shapes to create pictures of common objects and use

straws and clay to create models of two- and three-dimensional objects in their environment.

MP.6 Attend to precision. Ordinal numbers provide students with vocabulary to precisely describe

the spatial organization of ten shapes in a straight line.

MP.7 Look for and make use of structure. Students make use of their understanding of a shape’s

attributes to build three-dimensional shapes from two-dimensional shapes.



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Overview of Module Topics and Lesson Objectives

Standards Topics and Objectives Days

K.CC.4d

K.G.5

K.G.2

K.G.4

A Building and Drawing Flat and Solid Shapes

Lesson 1: Describe the systematic construction of flat shapes using

ordinal numbers.

Lesson 2: Build flat shapes with varying side lengths and record with

drawings.

Lesson 3: Compose solids using flat shapes as a foundation.

Lesson 4: Describe the relative position of shapes using ordinal numbers.

4

K.G.6

K.G.1

K.G.4

B Composing and Decomposing Shapes

Lesson 5: Compose flat shapes using pattern blocks and drawings.

Lesson 6: Decompose flat shapes into two or more shapes.

Lesson 7: Compose simple shapes to form a larger shape described by an

outline.

Lesson 8: Culminating task—review selected topics to create a cumulative

year-end project.

4

End-of-Module Assessment: Topics A –B 2

Total Number of Instructional Days 10



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Terminology

New or Recently Introduced Terms

First, second, third, fourth, fifth, sixth, seventh, eighth, ninth, tenth (ordinal numbers)

Familiar Terms and Symbols4

Above, below, beside, in front of, next to, behind (position words)

Circle

Cube (three-dimensional shape)

Cylinder (three-dimensional shape)

Face (two-dimensional side of a shape )

Flat (two-dimensional shape)

Hexagon (flat figure enclosed by six straight sides) Rectangle (flat figure enclosed by four straight sides)

Solid (three-dimensional shape)

Cone (three-dimensional shape)

Sphere (three-dimensional shape)

Square (flat figure enclosed by four straight, equal sides)

Triangle (flat figure enclosed by three straight sides)

Suggested Tools and Representations

Pattern block activity cards or attribute block activity cards Three-dimensional shapes: cone, sphere, cylinder, and cube

Two-dimensional shapes: circle, hexagon, rectangle, square, and triangle

Scaffolds5

The scaffolds integrated into A Story of Units give alternatives for how students access information as well as

express and demonstrate their learning. Strategically placed margin notes are provided within each lesson

elaborating on the use of specific scaffolds at applicable times. They address many needs presented by

English language learners, students with disabilities, students performing above grade level, and students

performing below grade level. Many of the suggestions are organized by Universal Design for Learning (UDL)

principles and are applicable to more than one population. To read more about the approach to

differentiated instruction in A Story of Units, please refer to “How to Implement A Story of Units.”

4 These are terms and symbols students have seen previously.

5 Students with disabilities may require Braille, large print, audio, or special digital files. Please visit the website,

www.p12.nysed.gov/specialed/aim, for specific information on how to obtain student materials that satisfy the National Instructional

Materials Accessibility Standard (NIMAS) format.



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Assessment Summary

Type Administered Format Standards Addressed

End-of-Module

Assessment Task

After Topic B Constructed response with rubric K.CC.4d

K.G.5

K.G.6

Culminating Task Lesson 8 Collaborative project: Review selected

topics to create a cumulative year-end

project.

K.G.6



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KG RA DE


Mathematics Curriculum

GRADE K • MODULE 6

Topic A: Building and Drawing Flat and Solid Shapes

Date: 4/11/14 6.A

© 2013 Common Core, Inc. Some rights reserved. commoncore.org This work is licensed under aCreative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported.License.

Topic A

Building and Drawing Flat and Solid

ShapesK.CC.4d, K.G.5, K.G.2, K.G.4

Focus Standard: K.CC.4d Understand the relationship between numbers and quantities; connect counting to

cardinality.

d. Develop understanding of ordinal numbers (first through tenth) to describe the

relative position and magnitude of whole numbers.

K.G.5 Model shapes in the world by building shapes from components (e.g., sticks and clay

balls) and drawing shapes.

Instructional Days: 4

Coherence -Links from: GPK –M2 Two-Dimensional and Three-Dimensional Shapes

-Links to: G1 –M5 Identifying, Composing, and Partitioning Shapes

In this final kindergarten module, students will extend and build upon their learning about two- and three-

dimensional shapes from Module 2. Students use their knowledge about common features of flats and solids

to create, construct, and compose shapes by building and drawing. Throughout, they use ordinal numbers to

describe the systematic construction of their flats (K.CC.4d).

Lesson 1 asks students to apply their knowledge of shape attributes (number and type of sides and corners)

by constructing flat shapes using straws and clay (K.G.5). For example, when constructing a triangle, the

student uses three equal, unconnected straws and connects the endpoints to form a three-sided, closed

figure. This represents a departure from viewing the figure as being inclusive of the interior to now

considering the shape as represented only by the outline, a perspective that will eventually develop into

formal definitions of triangles, quadrilaterals, and polygons (e.g., a triangle is formally defined in Grade 4 as

consisting of three non-collinear points together with the three segments joining them). Students will use

ordination to thirds to tell the steps they take to build their flat shapes (K.CC.4d).

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Topic ANYS COMMON CORE MATHEMATICS CURRICULUM K

Topic A: Building and Drawing Flat and Solid Shapes

Date: 4/11/14 6.A

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In Lesson 2, students investigate whether varied side length affects their ability to construct a shape. “What

happens if I use two long straws and one short straw to build my triangle?”

3 equal straws 3 unequal straws

Lessons 3 and 4 build upon the comparisons students made between two- and three-dimensional shapes in

Module 2 (K.G.4). In Lesson 3, students use the flats created from straws and clay in Lesson 1 as the

foundation for composing solids that model real world shapes and figures (K.G.5). They use these solids to

count faces, edges, and corners. In Lesson 4, they relate spatial understanding (relative position) and number

(magnitude) by using ordinal numbers to describe the position of flat shapes within a set of 10 (K.CC.4d).

A Teaching Sequence Towards Mastery of Building and Drawing Flat and Solid Shapes

Objective 1: Describe the systematic construction of flat shapes using ordinal numbers.(Lesson 1)

Objective 2: Build flat shapes with varying side lengths and record with drawings.

(Lesson 2)

Objective 3: Compose solids using flat shapes as a foundation.

(Lesson 3)

Objective 4: Describe the relative position of shapes using ordinal numbers.

(Lesson 4)

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Lesson 1: Describe the systematic construction of flat shapes using ordinal

numbers.

Date: 4/11/14

6.A

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Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 1NYS COMMON CORE MATHEMATICS CURRICULUM K

Lesson 1

Objective: Describe the systematic construction of flat shapes using ordinal

numbers.

Suggested Lesson Structure

Fluency Practice (12 minutes)

Application Problem (5 minutes)

Concept Development (25 minutes)

Student Debrief (8 minutes)

Total Time (50 minutes)


Count to 100 by Ones K.CC.1 (3 minutes)

If You’re Happy and You Know It K.CC.4d (5 minutes)

Peek-a-Boo Shapes K.G.2 (4 minutes)

Count to 100 by Ones (3 minutes)

Materials: (S) Rekenrek dot paper (fluency template)

Note: This activity maintains the rote counting skills acquired in GK –Module 5, and calls attention to the

structure of numbers to 100 with the use of the Rekenrek’s rows of 10 and the verbal cue as they cross

decades.

Students count to 100 (or as high as they can in three minutes) by touching the beads on the Rekenrek dot

paper. Have them say buzz after the last number of each row.

If You’re Happy and You Know It (5 minutes)

Note: This fun, familiar song gives students the opportunity to practice putting events in sequence, preparing

them for today’s work with ordinal numbers and step-by-step procedures.

T: Raise your hand if you know the song “If you’re happy and you know it.”S: (Raise hands.)

T: Even if you don’t know all of the words, you can still do all of the moves, and that’s the part that will

help us in math today. We’ll sing the song three times, and use a different movement each time.

Then, we’ll sing it a final time, and put all three movements together. Ready?

Verse 1: If you’re happy and you know it, clap your hands. (Clap, clap.)

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NOTES ON

MULTIPLE MEANS OF

REPRESENTATIONS:

Help English language learners work

with partners by giving them sentencestarters such as, “This is a ___ because

it has ___ sides,” and “I drew a ___

which has ___ corners.” Be sure to

post labeled pictures of shapes on the

word wall for students to refer to.

Verse 2: If you’re happy and you know it, stomp your feet. (Stomp, stomp.)

Verse 3: If you’re happy and you know it shout hooray . “Hooray!”

Verse 4 (combined): If you’re happy and you know it do all three. (Clap, clap. Stomp, stomp.)

“Hooray!” Invite students to make up three new verses and actions, then combine all three at the end.

Peek-a-Boo Shapes (4 minutes)

Materials: (T) Paper cutouts of triangles, rectangles, squares, hexagons, and circles (variety of sizes, including

exemplars, non-examples, and variants), pictures of objects that have flat shapes

Note: This quick review of the work of GK –Module 2 prepares students to work with flat shapes in today’s

lesson.

Show students each shape briefly, and then take it out of view. Remind students beforehand that they are to

use the listen, think, raise your hand, wait for the snap procedure to name the shape in choral response. Start

with easy shapes to build confidence, and then steadily increase the level of difficulty. After they have named

the shapes, have students tell the number of sides.


Materials: (S) Markers, paper

We are going to be talking about shapes again! Draw several

things you saw this past week that looked like shapes you know.

What are the different shapes called?

Share your picture with your partner. Talk about each of theshapes and how you knew its name. Does your partner agree

with you?

Note: Use this time to review the definitions of squares, circles,

rectangles, triangles, and hexagons with the students. Circulate

to ensure accuracy in the students’ definitions and precision in

their discussions. Coupled with the fluency work, the

Application Problem will serve as a brief review prior to

construction of shapes in today’s lesson.


Materials: (S) 15 coffee stir sticks or similar material marked at the midpoint with permanent marker,

scissors, small ball of clay, pencil, piece of construction paper, ruler

T: Listen to my directions. First, stand up. Second, put your hands on your shoulders. Go!

S: (Stand up and then put hands on their shoulders.)



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NOTES ON

MULTIPLE MEANS OF

ENGAGEMENT:Scaffold below grade level students’

understanding of ordinal numbers by

modeling for them. Ask students to

get up one at a time to demonstrate

first in line, second in line, and third in

line. Have students practice saying

who is first, second, and third in line as

you point to each corresponding

student.

T: What did I ask you to do first?

S: Stand up!

T: What was the second thing I asked you to do?

S: Put our hands on our shoulders.T: Good! Please sit down. Listen to my directions. First,

stand up. Second, put your hands on your shoulders.

Third, jump up and down! (Allow time for activity.)

Please sit down. What did I ask you to do first?

S: Stand up!

T: What was the second thing I asked you to do?

S: Put our hands on our shoulders.

T: And the third thing?

S: Jump up and down!

T: Good listening! Let’s play one more time. Listen carefully! First, claptwo times. Second, stomp three times. Third, shout “Hooray!” once.

(Allow time for activity.) What did you do first?

S: Clapped two times!

T: Second?

S: We stomped three times!

T: Third?

S: We shouted “Hooray!”

T: You are going to be builders today. We are going to be making

shapes. Look at the materials you have. What do you notice?

S: We have some sticks!

There is clay, too.T: Pick up your sticks and arrange them on your desk. Try

to make a shape. Who has an idea?

S: I used four sticks. I made a square.

T: How do you know it is a square?

S: There are four sides, and they are all the same! It

has four corners. It is closed.

T: Did anyone think of something else?

S: I only used three sticks. I made a triangle.

T: How do you know it is a triangle?

S: There are three straight sides.

There are threecorners, and they are all connected.

T: We are going to practice more shape-making.

First, use your scissors to cut each of your sticks at the mark in

the middle.

Second, arrange your little sticks to make different flat shapes.

MP.6

First

Second

Third



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Third, use bits of clay to connect the corners of your new shapes.

T: If you haven’t made a square already, please do so now. Then, you may experiment. How many

different shapes can you make? We will have a shape show when you are done. (Allow ample time

for experimentation and construction.)

T: Who would like to share one of their shapes? Tell us what you did first, second, and third. Use your

math words!

S: I made a triangle! First, I cut the sticks. Second, I picked three

sticks for the sides. Third, I stuck them together with clay!

S: I made a hexagon. First, I cut the sticks. Second, I chose six and

put them on my desk. Third, I used balls of clay to connect them.

T: Listen again. Get your pencil and construction paper ready. First,

put a dot on the left side of your paper. Second, draw a line that

starts at that dot with your ruler. Third, draw another line that

starts at the same dot with your ruler.

S: (Work.)T: Show me your work.

S: (Show their work.)

T: Listen again. First, put a dot at the ends of both your lines.

Second, draw a line with your ruler to connect those dots. Third,

show your work to a friend and tell him or her what shape you

drew. (Allow time for sharing.)

T: Now, share about all your shapes with your friends, the ones we

made with straws and the one we made with your ruler.

Allow time for sharing and discussion. If students built shapes with five

sides, or more than six sides, casually mention the name of the shape. Five sides is a pentagon. Seven sides is

a heptagon. Eight sides is an octagon. Nine sides is a nonagon. Ten sides is a decagon.

T: Listen carefully. First, put your name on your construction paper. Second, carefully lift your shapes

onto your paper. Third, stand up and get ready to look at the shapes the rest of the class created!

It’s time for a shape show! (Allow students to circulate to view and discuss one another’s work.

Encourage mathematical discussion and precision in vocabulary. When they are done, move the

papers carefully to a part of the room where they may be saved for use in Lesson 3 of this module.)



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Problem Set (10 minutes)

Students should do their personal best to complete the

Problem Set within the allotted 10 minutes.


Lesson Objective: Describe the systematic construction of

flat shapes using ordinal numbers.

The Student Debrief is intended to invite reflection and

active processing of the total lesson experience.

Invite students to review their solutions for the Problem

Set. They should check work by comparing answers with a

partner before going over answers as a class. Look for

misconceptions or misunderstandings that can beaddressed in the Debrief. Guide students in a

conversation to debrief the Problem Set and process the

lesson.

You may choose to use any combination of the questions

below to lead the discussion.

What words did we use to help us complete our

Problem Set in order?

What was the first thing we did in our Problem

Set? Did everyone draw a line to complete the

triangle first, before they colored their trianglegreen?

Look at the triangles and squares you drew in

your Problem Set. Are all the sides equal in

length? Find someone who drew their shapes

with equal length sides; find someone who drew

their shapes with unequal length sides.

How did the words first, second, and third help

us be good builders today?

Can you think of a time when order is important?

What would happen if we put our shoes on first

and our socks on second?

Can you think of other ways that we use words

like first, second, and third ?



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Exit Ticket (3 minutes)

After the Student Debrief, instruct students to complete the Exit Ticket. A review of their work will help you

assess the students’ understanding of the concepts that were presented in the lesson today and plan more

effectively for future lessons. You may read the questions aloud to the student.



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Lesson 1 Problem SetNYS COMMON CORE MATHEMATICS CURRICULUM K•6


numbers.

Date: 4/11/14

6.A



Name Date

Listen to the directions.

First, draw the missing line to finish the triangle using a ruler. Second,

color the corners red. Third, draw another triangle.

First, use your ruler to draw 2 lines to make a square. Second, color the

corners red. Third, draw another square.

First, draw a triangle using your ruler. Second, draw a different triangle

usin our ruler. Third, show our ictures to our artner.



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4 + 1 = ____

____ = 2 + 1

3 + 2 = ____

3 + 1 = ____

____ = 5 + 0

5– 1 = ____

____ = 4 – 1

3 – 2 = ____

3 – 0 = ____

____ = 5 – 4

2– 1 = ____

____ = 3 – 3

1 – 0 = ____

3–

0 = ____ ____ = 4 – 4

2 + 2 = ____

____ = 5 – 3

1 + 1 = ____

4–

0 = ____ ____ = 4 + 1



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Lesson 1 Exit TicketNYS COMMON CORE MATHEMATICS CURRICULUM K•6


numbers.

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Name Date

Use your ruler.

First, draw a straight line from the dot.Second, draw a different straight line from the dot.

Third, draw another straight line to make a triangle.



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Lesson 1 HomeworkNYS COMMON CORE MATHEMATICS CURRICULUM K•6

Name Date

First, draw 2 lines to make a rectangle.

Second, put a red circle on all the corners.

Third, put an X on the longer sides.

Follow the directions.

First, use your ruler to draw a line

finishing the triangle.

Second, color the triangle green.

Third, use your ruler to draw a

bigger triangle next to the green

First, draw a line to complete the hexagon.

Second, color the hexagon blue.

Third, write the number of sides the

hexagon has in the box below.

On the back of your paper draw:A shape with 3 straight sides.

A shape with 4 straight sides.

A shape with 6 straight sides.



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Lesson 1 Fluency TemplateNYS COMMON CORE MATHEMATICS CURRICULUM K•6


numbers.

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Lesson 2: Build flat shapes with varying side lengths and record with drawings.

Date: 4/11/14 6.A

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This work is licensed under a


Lesson 2

Objective: Build flat shapes with varying side lengths and record with

drawings.







Sprint: Core Fluency K.OA.5 (9 minutes)

Compose Teen Numbers K.NBT.1 (3 minutes)

Sprint: Core Fluency (9 minutes)

Materials: (S) Core Fluency Sprint A, B, C, or D

Note: This activity continues students’ progress toward mastery of the required fluency for kindergarten.

Decide on a core fluency skill in which students would benefit from extra practice: addition, subtraction, ormixed addition with subtraction within 5. Select the Sprint that is most appropriate for the class: Core

Fluency Sprint A, B, C, or D in the materials that follow. In order to correct the work as a class, all students

take the same Sprint.

T: It’s time for a Sprint! (Briefly recall previous Sprint preparation activities, and distribute Sprints

facedown.) Take out your pencil and one crayon, any color. (Demonstrate the first problem as

needed.)

Continue to follow the familiar Sprint procedure. Have students work on the same Sprint a second time.

Continue to emphasize that the goal is simply to do better than the first time and celebrate improvement.

Compose Teen Numbers (3 minutes)

Materials: (T) Hide Zero cards (optional)

Note: This maintenance activity ensures that students stay sharp on the work of the previous module.

T: (Show cards, or say the numbers 10 and 6.) Raise your hand when you can say the number the Say

Ten way. (Wait for all hands to go up, then signal.) Ready?



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NOTES ON

MULTIPLE MEANS OF

ACTION ANDEXPRESSION:

As more shapes are introduced, be

sure to put the shapes with pictures or

models on the word wall. This will help

English language learners study the

names of the shapes and allow

teachers to point to the shapes while

talking about them, making a clear

connection between the words and the

meaning.

S: Ten 6.

T: Now say it the regular way, please.

S: 16.

T: (If using Hide Zero cards, slide them together to formthe number 16.)

Continue with the following sequence: 17, 18, 19, 13, 14, 15,

11, 12, 10, 20.

Variation: Students can write the number bond, or write two

addition sentences on their personal boards.


Materials: (S) Approximately 15 coffee stir sticks, scissors,

personal white board, small ball of clay

T: Who can remind us about what we did in math class

yesterday? Can you use your math words to tell us, in

order, the steps that we took in our lesson?

S: First, we cut our sticks. They were all the same length!

Second, we made flat shapes with them on our

desks. Third, we stuck the ends together with clay

at the corners.

T: That’s right. We are going to make more flat shapes today.

Yesterday, we made special rectangles that had equal sides. What

did we call them?S: Squares.

T: Today, use your sticks and your clay to create another type of

rectangle, one that has corners like an L but whose sides are not all

the same length.

T: (Pause.) You may cut one or two of your sticks if you need to.

(Allow time for students to plan and create the shape. Circulate to

support students who may need further assistance.) Hold up your

rectangles! How do you know they are rectangles?

S: It looks like a square but the lengths of the sides are not the same!

It has two longer sides and two shorter sides. I had to cut one

of my sticks in half! They have corners that look like an L. Ithas four sides.

T: Take three sticks that are the same length. Now use those sticks to

make a closed shape with three straight sides. (Allow time for

students to experiment.) Hold up your shapes. What do we call this

shape?

MP.4



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NOTES ON

MULTIPLE MEANS OF

ENGAGEMENT:

Students with disabilities who might

have difficulty with fine motor

activities could benefit from using a

geoboard and rubber bands to make

different shapes or by allowing them to

use interactive technology such as theone found at

http://www.glencoe.com/sites/commo

n_assets/mathematics/ebook_assets/v

mf/VMF-Interface.html.

(In the Select Grade drop-down menu,

click Kindergarten. In the

Manipulatives drop-down menu, click

Geoboard/Bands.)

S: It is a triangle!

T: What if you take one of the sides of your triangle, cut it to be shorter and then put one of the pieces

back into your shape? (Allow time for students to experiment.) What do you notice?

S: It is still a triangle.

It just has one side that is shorter.

It looks pointier, but it still has threesides and three corners. Two sides are the same length!

T: Great job! With your partner, use your sticks and your

clay to make several different flat shapes. You may cut

the sticks to be any lengths you like. Be creative!

(Allow ample time for student work. Encourage

students to think about not only convex but also

concave figures. Hold up any interesting examples you

observe for extra inspiration. Again, if students ask,

casually mention the names of created shapes they

may not have studied yet.)

T: Wow! You made a lot of different shapes! Would

anyone like to show their favorite and tell the class

about it? (Allow time for discussion.)

T: With your ruler and your marker, try to copy each of

your new shapes on your board.

Allow time for students to replicate their shapes on paper.

Circulate to offer assistance to students who may still need help

in keeping their rulers straight and still during construction. If

time permits, allow students to turn and talk to their partners to

describe the shapes they drew.





Lesson Objective: Build flat shapes with varying side

lengths and record with drawings.

The Student Debrief is intended to invite reflection and

active processing of the total lesson experience.

Invite students to review their solutions for the Problem

Set. They should check work by comparing answers with a

partner before going over answers as a class. Look for

misconceptions or misunderstandings that can be

addressed in the Debrief. Guide students in a

conversation to debrief the Problem Set and process the

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lesson.

You may choose to use any combination of the questions below to lead the discussion.

Look at all the triangles on your Problem Set. Tell

your partner what they all have in common.Choose two triangles that are different. Tell your

partner how they are different.

Does a triangle need to be closed? Can it have

gaps between the sides?

I heard you say that all of the triangles are closed

and have three sides and three corners. Do they

all look the same? Tell your partner how many

different looking triangles you think you could

draw.

When you made a shape with four straws and

corners like an L, what did you call it? What didyou call the special shape you made where all

four straws were the same length?

(Hold up a set of three equal straws and a set of

three straws with different lengths.) If I asked

you to make a triangle, which set of straws would

you choose? Why?

Look carefully at your flat shapes and at those of

your peers. What are some ways we could sort

them? (Take time to allow several iterations of shape-sorting with the students. Encourage them to

be creative in their thinking. Apart from the number of sides, also guide them to think about

attributes such as concave vs. convex, regular vs. irregular, etc.)



assess the students’ understanding of the concepts that were presented in the lesson today and plan more

effectively for future lessons. You may read the questions aloud to the students.



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Lesson 2 Core Fluency Sprint ANYS COMMON CORE MATHEMATICS CURRICULUM K•6


Date: 4/11/14 6.A




Name Date

Write the missing number.

1 2 + 1 = 11 = 3 + 2

21 + 1 =

121 + 3 =

31 + 4 =

13= 2 + 2

43 + 1 =

14 = 1 + 2

52 + 2 =

151 + 4 =

62 + 3 =

16= 2 + 3

7 1 + 2 = 17 = 5 + 1

84 + 1 =

185 + 2 =

9 3 + 2 = 19 1 + 0 =

10 1 + 3 = 20 5 + 0 =

Number correct:



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Lesson 2 Core Fluency Sprint BNYS COMMON CORE MATHEMATICS CURRICULUM K•6


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Name Date


1 2 - 1 = 11 = 4 - 2

24 - 1 =

125 - 3 =

35 - 1 =

13= 3 - 1

43 - 1 =

14= 5 - 2

53 - 2 =

154 - 1 =

64 - 2 =

16= 5 - 4

75 - 3 =

17= 5 - 1

85 - 2 =

186 - 1 =

94 - 3 =

191 - 0 =

10 5 - 4 = 20 5 - 5 =

Number correct:



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Lesson 2 Core Fluency Sprint CNYS COMMON CORE MATHEMATICS CURRICULUM K•6


Date: 4/11/14 6.A




Name Date


1 2 + 1 = 11 3 + 2 =

22 - 1 =

123 - 2 =

33 + 1 =

134 + 0 =

43 - 1 =

144 - 0 =

54 + 1 =

155 + 0 =

64 - 1 =

165 - 0 =

71 + 1 =

175 - 5 =

81 - 1 =

184 + 1 =

9 2 + 2 = 19 5 - 4 =

102 - 2 =

205 - 1 =

Number correct:



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Lesson 2 Core Fluency Sprint DNYS COMMON CORE MATHEMATICS CURRICULUM K•6


Date: 4/11/14 6.A

© 2013 Common Core, Inc. Some rights reserved. commoncore.org


Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Un ported License.

Name Date


1 2 + 1 = 11 = 1 + 2

24 + 1 =

125 + 0 =

35 - 1 =

13= 3 - 1

43 + 1 =

14= 2 + 2

53 + 2 =

154 - 1 =

64 - 2 =

16= 5 - 4

75 - 3 =

17= 5 - 1

85 - 2 =

183 + 0 =

92 + 3 =

191 - 0 =

105 - 4 =

205 - 5 =

Number correct:



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Name Date

First, use a ruler to trace the shapes. Second, draw the shapes using your

ruler following the directions in the box.

Draw 2 different rectangles.

Draw 3 different triangles.

Draw 1 hexagon.



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5– 4 = ____

5 – 3 = ____

5 – 2 = ____

5 – 1 = ____

5 – 0 = ____

0 + 1 = ____

1 + 1 = ____

2 + 1 = ____

3 + 1 = ____

4 + 1 = ____

4– 2 = ____

2 – 1 = ____

3 – 2 = ____

3–

1 = ____5 – 0 = ____

4– 3 = ____

2 + 1 = ____

3 + 2 = ____

4–

1 = ____5 – 4 = ____



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Name Date

First, draw a triangle so all of the sides are different lengths.

Second, draw a triangle with your ruler that has 2 sides that are about the

same length.



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Name Date

Trace the shapes. Then use a ruler to draw other related shapes on your

own in the large rectangle. Draw more shapes on the back of your paper if

you would like!



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Lesson 2 Hide Zero CardsNYS COMMON CORE MATHEMATICS CURRICULUM K•6

Hide Zero Cards. Copy double-sided.

Numerals

1 0

0 1 2 3

4 5 6 7

8 9



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Lesson 2 Hide Zero CardsNYS COMMON CORE MATHEMATICS CURRICULUM K•6

Hide Zero Cards. Copy double-sided.

5-groups



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Lesson 3

Objective: Compose solids using flat shapes as a foundation.








Color by Answer Addition K.OA.5 (6 minutes)

Color by Answer Subtraction K.OA.5 (6 minutes)

Color by Answer Addition (6 minutes)

Materials: (S) Copies of the Fluency Problem Set, crayons

Note: This activity gives students an opportunity to practice the core fluency of addition within 5, and calls

students’ attention to the patterns within the chart.

After giving clear instructions and demonstrating a few problems as needed, allow students time to work

independently. Early finishers can analyze the patterns they see within the chart.

Color by Answer Subtraction (6 minutes)

Materials: (S) Copies of the Fluency Problem Set, crayons

Note: This activity gives students an opportunity to practice the core fluency of subtraction within 5, and calls

students’ attention to the patterns within the chart.

Conduct as above.


Materials: (S) Geoboard and rubber bands per pair (or dot paper, markers, ruler if geoboards are not

available)



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NOTES ON

MULTIPLE MEANS OF

ENGAGEMENT:Below grade level students, as well as

students with disabilities, will benefit

from extra practice creating a variety

of three- and four-sided shapes. Give

them extended time with a geoboard,

or make time for using interactive

technology as that found at

http://www.mathlearningcenter.org/w

eb-apps/geoboard/.

You have a challenge today! Work with your partner. On your

geoboard, make a shape with three sides. Now leave your

shape on your board and let your partner make a three-sided

shape as well. Do they look the same? Name the shapes.

Now make a shape with four sides. Have your partner make

another four-sided shape. Do they look alike? Name the

shapes.

Try it with five sides! Then, six! How far can you and your

partner go?

Note: Reviewing the construction of a variety of flat shapes will

serve as the anticipatory set for extending a flat shape into a

solid in today’s lesson.


Materials: (T) Set of geometric solids (S) Student squares from GK –M6 ─ Lesson 1, 12 coffee stir sticks, small

ball of clay

Part 1: Review the attributes and names of solids.

T: (Hold up each solid as a review exercise.) What do we call this solid?

S: A cone!

T: How did you know?

S: It looks like an ice cream cone. It looks like the orange cones in

the lunch area.

T: What is special about a cone? Talk to your partner.

S: It has a circle on the bottom. It rolls funny, not in a straight line

like a ball. It kind of looks like a triangle when you look at it from the side. It’s flat on the

bottom, smooth, and round in the middle and pointy on the top.

Continue reviewing the other solids, asking students to explain how they knew the name of the solid and to

describe its attributes.

Part 2: Construct a cube.

T: In our last lesson you made some great shapes out of your straws! I want to use some of the squares

you constructed to make a new shape like one of our solids. Does anyone have any ideas?

S: Maybe we could make something like a cube! You could use one square to be on the bottom likethe floor of a room. Some of the others could be like the faces. We need one for the top, too.

T: Look at the cube we already have. (Hold it up.) How many squares will I need to use? Let’s count

together.

S: 1, 2, 3, 4, 5, 6.

T: Let’s use this one as the bottom of the cube. Now, I will use some of your other squares for the

MP.7

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sides. (Demonstrate.) What does it look like now?

S: It looks like a box. It is still open, though.

T: What if I trace one of the squares on my paper and cut it out? (Demonstrate.)

I will attach it to one of the squares. (Cover one side of the skeleton with thepaper to create a face and hold the shape up for observation.) What do you

notice?

S: It fits. We still need more faces to close it up!

T: I will trace and cut some more. (Demonstrate with the remaining 5 faces to

create a cube.)

T: Let’s double-check. How many faces do we have? First let’s count the faces

on the top and bottom. Say what we are counting.

S: (Point and touch.) 1 face, 2 faces.

T: Second, let’s count the ones around the middle. This is our third face so start

at the number?

S: 3!

T Go.

S: 3 faces, 4 faces, 5 faces, 6 faces.

T Have we counted all of the faces? Did we miss any? How many faces are

there on the cube?

S: 6 faces.

T: Now count the edges for me. First we’ll count the ones on the bottom. I’ll

start with this one.

S: (Touch as they count.) 1 edge, 2 edges, 3 edges, 4 edges.

T: Second, let’s count the edges in the middle. Start at the number after 4.

S: 5 edges, 6 edges, 7 edges, 8 edges.

T: Third, let’s count the ones at the top. How many edges have we counted so

far?

S: 8.

T: So, the next edge we count will be number…?

S: 9!

T: Count when I touch.

S: 9 edges, 10 edges, 11 edges, 12 edges.

T: Are there any more edges?

S: No!

T: Tell your partner how we counted. What did we do first, second, and third?

S: First, we counted the edges on the bottom. Second, we counted the ones in

the middle. And third, we counted the edges on the top.

T: Let’s count them once more without stopping and without saying what we

are counting.

Counting Faces

Counting Edges

Counting Corners

MP.7



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S: (Touch systematically as students count.) 1, 2, …11, 12.

T: Now count the corners. (Repeat the same process with the corners, having them count the corners

on the bottom and then the top, saying what they are counting.)

T: It is time to make a shape like this on your own. Begin by making a square out of your straws for thebottom. Make another one for the top, too. (Allow time for students to work.)

T: What do we need now?

S: We need to make the edges. Let’s stick straws into the corners of our

bottom squares so they are poking up. They will look like table legs.

Then we can put on the top!

T: Please finish your shapes. (Allow time for students to construct the shape.

Circulate to observe understanding and offer support as necessary.)

T: You have made wonderful shapes! Hold them up. What do you notice

about them?

S: They look like little boxes! They are the same on every side.

T: Work with your partner to count the faces, edges, and corners of your pretend cube like we didearlier.

T: (Circulate and support the counting, which is challenging for kindergarten students.) What shapes

are the invisible faces?

S: They are all squares.

T: I wonder what would happen if we put two of these shapes together. With your partner, see what

you can create if you use more than one.

S: Now ours is taller, like a building! Ours looks like a train.

T: What are the shapes of the new invisible faces?

S: Squares. Rectangles!

T: Wait for my signal. How many corners do youhave now? Count them using our system. (Signal

and give students sufficient time to count.)

S: 8 corners.

T: How many faces? (Give students time to count.)

S: 6 faces!

T: How many edges? (Give students time to count.)

S: 12 edges!

T: Great work. Take a minute to compare your new

shape with another pair’s.

S: (Compare shapes.)




MP.7



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Lesson Objective: Compose solids using flat shapes as a foundation.

The Student Debrief is intended to invite reflection and active processing of the total lesson experience.

Invite students to review their solutions for the Problem Set. They should check work by comparing answers

with a partner before going over answers as a class. Look for misconceptions or misunderstandings that can

be addressed in the Debrief. Guide students in a conversation to debrief the Problem Set and process the

lesson.

You may choose to use any combination of the questions below to lead the discussion.

How many squares did you trace on your Problem Set before you started cutting? What did you

have to do to make a cube out of all the squares you traced?

What two shapes did you trace to make your cylinder? (Circle and rectangle.) What happened to

the rectangle when you cut and folded the paper to make the cylinder? Could we say that a

rectangle is a face of a cylinder? Why or why not? (No. Faces are flat. Once we roll up therectangle to make a cylinder, it is no longer flat.) What about the circle? Is a circle a face of the

cylinder?

When you counted the faces of your cube, how did you keep track of your count? How did you

make sure that you didn’t count any face twice?

Describe a cube to me. Tell me about its faces, edges, and corners.

Describe a cylinder to me. Tell me about its faces, edges, and corners.



assess the students’ understanding of the concepts that were presented in the lesson today and plan moreeffectively for future lessons. You may read the questions aloud to the students.



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Lesson 3 Fluency Problem SetNYS COMMON CORE MATHEMATICS CURRICULUM K•6

Name Date

Add. Color the blocks using the code for the total.

1-RED 2-ORANGE 3-YELLOW

4-GREEN 5-BLUE

0 + 1 1 + 1 2 + 1 3 + 1 4 + 1

0 + 2 1 + 2 2 + 2 3 + 2

0 + 3 1 + 3 2 + 3

0 + 4 1 + 4

0 + 5



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Lesson 3 Fluency Problem SetNYS COMMON CORE MATHEMATICS CURRICULUM K•6


Date: 4/11/14 6.A



Name Date

Subtract. Color the blocks using the code for the difference.

0-PURPLE 1-RED 2-ORANGE 3-YELLOW

4-GREEN 5-BLUE

1 - 0 2 – 0 3 – 0 4 – 0 5 – 0

1 - 1 2 – 1 3 – 1 4 – 1 5 – 1

2 - 2 3 – 2 4 – 2 5 – 2

3 – 3 4 – 3 5 – 3

4 – 4 5 – 4

5 - 5



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Name Date

Trace the circles and rectangle. Cut out the shape. Fold and tape to create acylinder.



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Trace the squares. Cut out the shape. Fold and tape to create a cube.



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Name Date_____________

Draw a line from the flat shape to the object that has a face with that

flat shape.



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Name Date

Draw something that is a cylinder.

Circle the flat shape you can see in a .

Draw something that is a cube.




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Draw something that is a cone.


Draw a 3-dimensional solid. Draw one of your solid’s faces. Tell an adult

about the shapes you drew.

Note to Family Helpers: Your student knows how to name some three-dimensional solids:

cylinders, cones, cubes, and spheres. You can often find these 3D shapes around the house in

objects like soup cans, ice cream cones, boxes, and balls. For the last question, it is acceptable

for your student to find and draw a different type of three-dimensional solid. Talk about the

number of edges, corners, and faces on the object.



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Lesson 4: Describe the relative position of shapes using ordinal numbers.

Date: 4/11/14 6.A




Lesson 4NYS CO

Math Gk m6 Full Module

Documents

Transcript of Math Gk m6 Full Module